The former prime minister will argue that Theresa May is trying to avoid spelling out the detail of her plans until “we are irreversibly out of Europe”.
He will say Parliament has the chance to “change the direction of the process” by legislating for another referendum on the terms of the Brexit deal.
The ex-PM will say: ”People say that there will be disillusion if Brexit doesn’t happen. Personally, I doubt this if it is the result of a fresh ‘say’ on the final deal.
“But even if true, the bigger disillusion will be when those who voted for Brexit because they feared the future shaped by free market globalisation, realise they are now conscripts in an adventure to embrace it more fully.
“This is the awesome responsibility which now rests with Parliament.”
Mr Blair’s latest intervention comes after Owen Smith was sacked from Jeremy Corbyn’s shadow cabinet after calling for a second public vote, risking deepening divisions within Labour over the approach to Brexit.
In a speech in Westminster, Mr Blair will say the Government’s whole approach to the negotiation so far has been based on trying to satisfy both wings of the Conservative Party.
The approach has become known as “cakeism” over claims the Government is trying to “have its cake and eat it” .
Mr Blair will say: “As time goes on, it will become crystal clear that the Government’s original negotiating position was built on sand.
“They will realise that they are in mortal danger of putting a proposition to Parliament which will not pass.
“Either it will mean divergence from Europe in which case, the business community will protest the damage and MPs may take notice of that.
“Or it will mean alignment with Europe in which case the diehard Brexiteers will cry foul and the British people will wonder why we are leaving.”
The approach will be to try to “fudge” the problem – supported by Brexiteers – until the date of the UK’s departure, Mr Blair will say.
Ministers will hope that the terms of the new relationship are “sufficiently vague to let the fiction of ‘cakeism’ continue”.
“It is this strategy that Parliament has a duty to foil,” Mr Blair will say, arguing that the Government’s approach is “deeply, dangerously irresponsible.”
The ex-premier will argue that the Government should spell out the choice facing the country – either a close relationship with the EU which would risk failing to fulfil the “central Brexit promise” of control over laws or divergence from Brussels which could disrupt trade and damage the economy.
He will say: “The sensible strategic course for the Tories is to share the responsibility.
“Resolve the dilemma before March 2019. Put the proposition to Parliament.
“If it succeeds, then no one can say we voted in Parliament in ignorance. Even better let the MPs have a free vote.
“Then let the people make the final judgment.”